{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第1章 统计学习方法概论"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "举例：我们用目标函数$y=sin2{\\pi}x$, 加上一个正态分布的噪音干扰，用多项式去拟合【例1.1 11页】\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy.optimize import leastsq\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ps: numpy.poly1d([1,2,3])  生成  $1x^2+2x^1+3x^0$*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 目标函数\n",
    "def real_func(x):\n",
    "    return np.sin(2*np.pi*x)\n",
    "\n",
    "# 多项式\n",
    "def fit_func(p, x):\n",
    "    f = np.poly1d(p)\n",
    "    return f(x)\n",
    "\n",
    "# 残差\n",
    "def residuals_func(p, x, y):\n",
    "    ret = fit_func(p, x) - y\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 十个点\n",
    "x = np.linspace(0, 1, 10)\n",
    "x_points = np.linspace(0, 1, 1000)\n",
    "# 加上正态分布噪音的目标函数的值\n",
    "y_ = real_func(x)\n",
    "y = [np.random.normal(0, 0.1) + y1 for y1 in y_]\n",
    "\n",
    "\n",
    "def fitting(M=0):\n",
    "    \"\"\"\n",
    "    M    为 多项式的次数\n",
    "    \"\"\"\n",
    "    # 随机初始化多项式参数\n",
    "    p_init = np.random.rand(M + 1)\n",
    "    # 最小二乘法\n",
    "    p_lsq = leastsq(residuals_func, p_init, args=(x, y))\n",
    "    print('Fitting Parameters:', p_lsq[0])\n",
    "\n",
    "    # 可视化\n",
    "    plt.plot(x_points, real_func(x_points), label='real')\n",
    "    plt.plot(x_points, fit_func(p_lsq[0], x_points), label='fitted curve')\n",
    "    plt.plot(x, y, 'bo', label='noise')\n",
    "    plt.legend()\n",
    "    return p_lsq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### M=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [-0.02696563]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=0\n",
    "p_lsq_0 = fitting(M=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### M=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [-1.34679124  0.64642998]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=1\n",
    "p_lsq_1 = fitting(M=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### M=3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [ 23.54070749 -35.69655526  12.43656224  -0.22443309]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=3\n",
    "p_lsq_3 = fitting(M=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### M=9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [-2.12879907e+04  9.94706450e+04 -1.94718497e+05  2.06856601e+05\n",
      " -1.29045928e+05  4.77347118e+04 -1.00136863e+04  1.03488206e+03\n",
      " -3.04686803e+01 -2.51427883e-01]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=9\n",
    "p_lsq_9 = fitting(M=9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当M=9时，多项式曲线通过了每个数据点，但是造成了过拟合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 正则化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "regularization = 0.0001\n",
    "\n",
    "\n",
    "def residuals_func_regularization(p, x, y):\n",
    "    ret = fit_func(p, x) - y\n",
    "    ret = np.append(ret,\n",
    "                    np.sqrt(0.5 * regularization * np.square(p)))  # L2范数作为正则化项\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 最小二乘法,加正则化项\n",
    "p_init = np.random.rand(9 + 1)\n",
    "p_lsq_regularization = leastsq(\n",
    "    residuals_func_regularization, p_init, args=(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ebaf2e6f80>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_points, real_func(x_points), label='real')\n",
    "plt.plot(x_points, fit_func(p_lsq_9[0], x_points), label='fitted curve')\n",
    "plt.plot(\n",
    "    x_points,\n",
    "    fit_func(p_lsq_regularization[0], x_points),\n",
    "    label='regularization')\n",
    "plt.plot(x, y, 'bo', label='noise')\n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
